Tooth enamel consists of hydroxyapatite, Ca5(PO4)3 OH (Ksp=6.8 ×10^-37) . Fluoride ion added to

step 1 First, we need to calculate the molar solubility of each species from the KSP expression. So we

Tooth enamel consists of hydroxyapatite, Ca5(PO4)3 OH...

Tooth enamel consists of hydroxyapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ $\left(K_{\mathrm{sp}}=6.8 \times 10^{-37}\right) .$ Fluoride ion added to drinking water reacts with $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ to form the more tooth decay-resistant fluorapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\left(K_{\mathrm{sp}}=1.0 \times 10^{-60}\right) .$ Fluoridated water has dramatically decreased cavities among children. Calculate the solubility of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ and of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}$ in water.

Tooth enamel consists of hydroxyapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ $\left(K_{\mathrm{sp}}=6.8 \times 10^{-37}\right) .$ Fluoride ion added to drinking water
reacts with $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ to form the more tooth decay-resistant fluorapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\left(K_{\mathrm{sp}}=1.0 \times 10^{-60}\right) .$ Fluoridated water has dramatically decreased cavities among children. Calculate the solubility of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}$ and of $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}$ in water.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant is a numerical value that represents the equilibrium between a solid and its dissolved ions in a saturated solution. It is defined by the product of the molar concentrations of the individual ions, each raised to the power of their stoichiometric coefficients, and it indicates the extent to which a compound will dissolve. Smaller Ksp values correspond to compounds that are less soluble in water.

Dissolution Equilibrium

Dissolution equilibrium occurs when a sparingly soluble compound dissolves in water to form its constituent ions, and these ions are in dynamic equilibrium with the undissolved solid. At this point, the rate of the dissolving process equals the rate of the precipitating process, as described by the equilibrium constant expression.

Molar Solubility Calculation

Molar solubility is the maximum number of moles of a compound that can dissolve per liter of solution to establish a saturated solution. It can be calculated by expressing the ion concentrations in terms of the molar solubility 's' according to the stoichiometry of the dissolution reaction, substituting these expressions into the Ksp expression, and solving for 's'.

Effect of Ionic Substitution on Solubility

Ionic substitution involves replacing one ion in a compound with another, which can significantly influence the solubility by altering the compound's lattice energy and the stability of the crystalline structure. Such changes are reflected in the Ksp values and can result in a compound being more or less resistant to dissolution.

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